Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
460 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11719100 | C2 | direct (N × H) |
| 5. C2×#88104 | C2 | semidirect |
| 6. C2×#88103 | C2 | semidirect |
| 25. #88104 | C22 | semidirect |
| 26. #88103 | C22 | semidirect |
| 131. C2×C13 | #430 | semidirect |
| 167. C13 | C2×#430 | semidirect |
| 217. C2 | #11719100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D13⋊M16 | 2 |
| C22×#6118 | 2 |
| C2×M16×D13 | 2 |
| #11719100 | 2 |
| C2×#88104 | 2 |
| C2×#88103 | 2 |
| C2×#430 | 13 |